This is probably not the kind of question you'll often encounter on this forum, but I think a bit of background is needed for this question to make sense and not seem like a duplicate:

2012 has been an annus horribilis in my life. I have lost a lot of close relatives in a sudden surge of cardiovascular diseases in my family. I also discovered I inherited genetic diseases and that I'll probably undergo the same fate sooner or later.

One of the people I've lost is my father. We used to talk about physics all the time, and ever since I was 5 I kept telling him my dream was contributing to the field. When I lost him a couple of months ago, I used studying as an emotional outlet. He always emphasized the importance of academic excellence, and for this reason I got obsessed with studying and getting high grades even more than I ever did.

I now am 1/80 in a top high school, but I am frustrated enormously. I find that I waste my time at high school, especially since I probably won't have as much time here as many other people do. I find the mathematics and physics boring and easy, and I feel like I'm wasting my time with certain classes which don't interest me at all (for example Latin). So I decided to study physics and mathematics outside of school. My school has been somewhat supportive, granting me a day per week off to do whatever I want, basically. I of course have a considerable amount of free time in addition to that day, since I ace almost every test without too much studying and without making my homework (not because I don't want to, but because I don't need to).

I decided to self-study because I decided that life is too short (and mine will be even shorter, if I reach 50 I'd be lucky) to waste time. So my plan is to do at least the first 2 years of undergraduate physics in the 2 years I've got left at my high school. My main objective is to gain a mathematical and physical understanding of quantum mechanics, as advanced as I possibly can.

I am currently studying Linear Algebra and Statistics, but I have a problem. I don't know what to study and, especially, in what order to study it. I have read literally read dozens of questions and answers as to what should be the mathematical/physical background for Quantum Mechanics (my future field of interest). But I find these to be too general, and I often am overwhelmed by it. In the same way you can get overwhelmed when you need to clean your house, but it’s so dirty that you don’t know where to start. So I would like your help.

My current mathematical background:

Basic differential calculus and no integral calculus, we will get that later on this year, however, I think it’s best for me to study it myself before we get it at school since it is crucial in physics. To show my level of differential calculus, this is about the toughest homework question we had to solve algebraically: Given are the functions $f_p(x) = \dfrac{9\sqrt{x^2+p}}{x^2+2}$. The line $k$ with slope $2.5$ touches the function of $f_p$ at point $A$ with $x_A=-1$. Get the function of $k$ algebraically.

Trigonometry and trigonometric functions. Again, as above, one of the toughest question we had to solve: Given are the functions $f(x)=-3+2cos(x)$ and $g(x)=cos(x-0.25\pi)-2$. Get the functions $s(x)=f(x)+g(x)$ and $v(x) = f(x)-g(x)$ in the form $y(x)=a+bcos(c(x-d))$.

And of course everything below this level. I probably forgot some things, but you can ask my in the comments if I know certain fields. We will get a lot more mathematics in the coming years, but I want you to disregard that fact when answering that questions. I want to self-study as much as I can, and my mathematics teacher is very fond of me, so if I know a topic before we get it in class, he will let me do other mathematics that I want (he even said this). So I won’t lose time by self-studying subjects we’ll get eventually, so don’t worry about that.

My current physics background (names of the chapters we discussed):

Newton’s laws, Mechanical energy/forces

Pressure and Heath

Signal processing

Electric currents (Ohm’s law, Series and parallel circuits, etc.)

Again, everything below this level too (again, I’m probably forgetting stuff). Here exactly the same thing counts as with mathematics, we will get a lot more physics in the coming year, but again, disregard that. My physics teacher adores me, even more so than my mathematics teacher, so again, he won’t mind if I do something else if I know the material he’s discussing already.

This is of higher level than American AP classes and British A-levels, keep that in mind.

Now my question is, what mathematics and physics do I need to study, and my importantly, in which order do I need to study it, in order to have a basic understanding of quantum mechanics in 2 years? I know basic is a very general term, but I think you people, as people who studied it themselves, know what is realistic and achievable. I know this might seem like a duplicate of hundreds of previous questions, but it isn’t. All the other people asking this question have gotten answers that I don’t find suitable for me. Mostly the answers are from people who assume that you have to ‘have a basic understanding of this, a basic understanding of that’, etc. But how do I know what ‘basic means’? Also, now that you guys know exactly what I know and what I don’t, you can more finely tune the answers into my personal situation. As I said, currently I am doing Linear Algebra and Statistics, so you can omit those 2 from your answers, and start from the point I finished those 2 (which will be around January).

p.s. If you want to recommend certain books, be my guest. If it's a good book, than money is no issue, I've saved up enough money throughout the years

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7

This is way too broad and rather off topic. We don't really recommend what to study here, we answer questions based on Physics concepts. If you want, ask in Physics Chat. Also, the entire life-story thing is a bit too long and irrelevant :)
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Manishearth♦Nov 24 '12 at 13:49

@Manishearth and people being critical, it is ok to be a bit human now and then instead of pedantic. The forum will not suffer and some moral support to a young person is good.
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anna vNov 24 '12 at 15:25

3

@PersonalVendetta do not angst over such hereditary problems as you describe, possibly by the time they can hit you medicine will have progressed to the point of eliminating the problems. Enjoy studying and exploring physics, it is a great adventure.
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anna vNov 24 '12 at 15:29

2

One piece of advice that someone should give: Learning mechanics and E&M in high school is quite do-able. But don't go rushing through the basics! Take the time to learn them deeply. Do as many problems as you can. Spend time studying and thinking about the solutions of the equations in as many situations as you can. Don't just be content with the Coulomb potential!
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user1504Nov 24 '12 at 17:14

4 Answers
4

Set your goals on something concrete that you really would like to know but do not yet understand at all, such as ''Why does water freeze?'' or ''What is an elementary particle?''.
(And if that is settled, go for something more advanced but again concrete, etc.)

Given the goal, search for the answer, starting with Wikipedia (and later Google Scholar), and backtracking on not or only partially understood concepts and topics until you feel firm ground. This is the only way to see what is important and why. It may take you years to fully understand the answers (some questions of this kind are still poorly understood even on the research level), but it will unlock all your intellectual capabilities, and make you an independent thinker.

You may also try my online book http://lanl.arxiv.org/abs/0810.1019,
for which I got several times feedback from 16 year olds who liked it.
If you lack some background, send me an email indicating what you don't understand, and I'll tell you how to learn that.

Whereas, I must say, it is not always possible. Put yourself in the position of a newby, then look for 'Chiral gauge' in Wikipedia and try to follow the concept...
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Eduardo Guerras ValeraNov 24 '12 at 17:08

The backtracking depth will be usually below a dozen, but one may need lots of such steps. I indicated this by saying that it may take years. But these years are very well spent, probably much better than following all details of a standard textbook.
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Arnold NeumaierNov 24 '12 at 17:14

Your history is deeply moving, so... I apologize for breaking the rules for once, answering here.

First, bear in mind that any life expectancy is a statistical quantity, but every single individual is a statistical fluctuation. If you have, for instance, an expectancy of 20 years in front of you, that only means that the average time left in a set of thousands men in your situation, or if you could rewind and live your life thousands times (that equivalence is called ergodicity) will be 20 years. But for a single individual, nobody can state anything. (After all, this answer turns out to be not fully "unscientific")

Second, please send me a mail. I have very good suggestions on self-learning physics. My address is in one of the comments (I will erase that comment soon).

I will make an unusual suggestion, just because no-one else will suggest proceeding in this way: You should make it your goal to understand the Higgs mechanism, both as a way to give masses to the W and Z bosons, and as a way to give masses to the elementary fermions (the details are different for the two cases).

The Higgs mechanism is a sufficiently advanced concept that to understand it will require you to learn quantum mechanics, special relativity, quantum field theory... so as a goal it is advanced enough to force you to learn all the things that you want to learn anyway. And it is newly validated as an aspect of the real world, so this is the right time to be learning how it works.